Linear magnetoelectric coupling

Linear Magnetoelectric Coupling and Ferroelectricity Induced by Flexomagnetic Effect in Ferroics... 

It follows from (4.44) that the linear FME coupling induced by the spatial confinement gives rise to additional size-dependent linear magnetoelectricity in... 

Linear Flexo-Magnetoelectric Coupling in Nanosized A ntiferromagnet-F erroelectrics... 

Note that not all antiferromagnets-ferroelectrics are linear MEs (e.g., 6 and > mm symmetry has j = 0) without consideration of the linear FME coupling. So, the linear FME coupling, induced either by the spatial confinement or by external bending, gives rise to the linear magnetoelectricity in the nanosized systems with, e.g., 6 and (y mm symmetry. 

One can find all the symmetry groups of antiferromagnets, which can be improper ferroelectrics due to nonzero flexomagnetic effect (in some instances Qij / 7 0) in the paper [96]. Note that seven of the groups have no conventional linear ME effect. So, the linear FME coupling gives rise to the size-dependent linear magnetoelectricity in the type-II multiferroic nanosystems. 

Fig. 4.34 Linear dielectric susceptibility (a, c) and magnetoelectric tunability (b, d) at increasing magnetic fields H / MK) = 0,0.1,0.2,0.5,0.7 (different curves) for cases of zero flexomagnetic coupling (a, b) and nonzero flexomagnetic coupling (c, d). Dashed curve is for zero magnetic field. Dimensionless parameters (4.46) values = 0, —0.2 (dotted and solid curves respectively).

---